Set functions are mappings that assign to subsets of a universal set a real number and
appear in many fields of mathematics (pure and applied) and computer sciences …

The paper establishes a formula for enumeration of curves of arbitrary genus in toric
surfaces. It turns out that such curves can be counted by means of certain lattice paths in the …

The first chapter deals with idempotent analysis per se. To make the pres-tation self-
contained, in the first two sections we define idempotent semirings, give a concise …

This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic
Geometry in October 2004. Tropical Geometry? rst appeared as a subject of its own in 2002 …

The central focus of this book is the control of continuous-time/continuous-space nonlinear
systems. Using new techniques that employ the max-plus algebra, the author addresses …

This paper is devoted to Idempotent Functional Analysis, which is an “abstract” version of
Idempotent Analysis developed by VP Maslov and his collaborators. We give a brief survey …

H∞ control originated in an effort to codify classical control methods where one shapes
frequency response functions to meet certain objectives. These techniques have dominated …

On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover,
the broken lines can be obtained as limits of those curves. The corresponding deformation …

This paper is a brief introduction to idempotent and tropical mathematics. Tropical
mathematics can be treated as the result of the so-called Maslov dequantization of the …

New hyperfields, that is fields in which addition is multivalued, are introduced and studied. In
a separate paper these hyperfields are shown to provide a base for the tropical geometry …